de Bruijn–Newman constant
E239168
The de Bruijn–Newman constant is a real number arising in the study of the zeros of the Riemann zeta function and related Fourier transforms, central to a refined form of the Riemann Hypothesis.
All labels observed (1)
| Label | Occurrences |
|---|---|
| de Bruijn–Newman constant canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2169628 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: de Bruijn–Newman constant Context triple: [N. G. de Bruijn, notableWork, de Bruijn–Newman constant]
-
A.
Gauss’s constant
Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
-
B.
Riemann–Siegel formula
The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
-
C.
Riemann zeta function
The Riemann zeta function is a complex-valued function central to analytic number theory, whose properties—especially the distribution of its zeros—are deeply connected to the distribution of prime numbers.
-
D.
Riemann hypothesis
The Riemann hypothesis is a famous unsolved conjecture in number theory asserting that all nontrivial zeros of the Riemann zeta function lie on a critical line in the complex plane, with deep implications for the distribution of prime numbers.
-
E.
Deuring–Heilbronn phenomenon
The Deuring–Heilbronn phenomenon is a result in analytic number theory describing how the presence of an exceptional (Siegel) zero of a Dirichlet L-function forces other zeros away from the real axis, sharpening zero-free regions and affecting the distribution of primes in arithmetic progressions.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: de Bruijn–Newman constant Target entity description: The de Bruijn–Newman constant is a real number arising in the study of the zeros of the Riemann zeta function and related Fourier transforms, central to a refined form of the Riemann Hypothesis.
-
A.
Gauss’s constant
Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
-
B.
Riemann–Siegel formula
The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
-
C.
Riemann zeta function
The Riemann zeta function is a complex-valued function central to analytic number theory, whose properties—especially the distribution of its zeros—are deeply connected to the distribution of prime numbers.
-
D.
Riemann hypothesis
The Riemann hypothesis is a famous unsolved conjecture in number theory asserting that all nontrivial zeros of the Riemann zeta function lie on a critical line in the complex plane, with deep implications for the distribution of prime numbers.
-
E.
Deuring–Heilbronn phenomenon
The Deuring–Heilbronn phenomenon is a result in analytic number theory describing how the presence of an exceptional (Siegel) zero of a Dirichlet L-function forces other zeros away from the real axis, sharpening zero-free regions and affecting the distribution of primes in arithmetic progressions.
- F. None of above. chosen
Statements (41)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical constant
ⓘ
real number ⓘ |
| appearsIn |
study of deformed Riemann xi functions
ⓘ
theory of entire functions of Laguerre–Pólya class ⓘ |
| characterization | threshold between all-real zeros and some non-real zeros for a family of entire functions ⓘ |
| conjecturedRelationToRiemannHypothesis |
Riemann hypothesis
ⓘ
surface form:
Riemann Hypothesis is equivalent to Λ ≤ 0
|
| conjecturedSign | nonnegative ⓘ |
| connectedTo |
Riemann xi function
ⓘ
distribution of zeros of entire functions ⓘ heat-flow deformation of entire functions ⓘ |
| definitionContext | deformation of the Riemann xi function by the heat equation ⓘ |
| field |
Fourier analysis
ⓘ
analytic number theory ⓘ complex analysis ⓘ |
| furtherDevelopedBy | Charles M. Newman ⓘ |
| hasInequalityFormulation | Λ ≥ 0 ⓘ |
| implication |
if Λ > 0 then some deformations of the xi function have non-real zeros
ⓘ
if Λ ≤ 0 then all zeros of the Riemann xi function are real ⓘ |
| introducedBy |
N. G. de Bruijn
ⓘ
surface form:
Nicolaas Govert de Bruijn
|
| knownLowerBound | Λ ≥ 0 ⓘ |
| knownLowerBoundProvedBy |
Brad Rodgers
ⓘ
Terence Tao ⓘ |
| knownLowerBoundYear | 2018 ⓘ |
| mathematicalDomain | theory of zeta and L-functions ⓘ |
| namedAfter |
Charles M. Newman
ⓘ
N. G. de Bruijn ⓘ
surface form:
Nicolaas Govert de Bruijn
|
| openProblem |
determine the exact value of Λ
ⓘ
prove or disprove Λ = 0 ⓘ |
| property | is the infimum of parameters t for which a deformed xi-function has only real zeros ⓘ |
| refinedConjecture | Λ = 0 ⓘ |
| relatedTo |
Fourier transform
ⓘ
Riemann hypothesis ⓘ
surface form:
Riemann Hypothesis
Riemann zeta function ⓘ entire functions with real zeros ⓘ zeros of the Riemann xi function ⓘ |
| role | measures how far the Riemann Hypothesis could fail ⓘ |
| status |
exact value unknown
ⓘ
sign known to be nonnegative ⓘ |
| symbol | Λ ⓘ |
| upperBound | less than 1 ⓘ |
| usedIn | refined formulations of the Riemann Hypothesis ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: de Bruijn–Newman constant Description of subject: The de Bruijn–Newman constant is a real number arising in the study of the zeros of the Riemann zeta function and related Fourier transforms, central to a refined form of the Riemann Hypothesis.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.